Adaptive Markov Control Processes
Adaptive Markov Control Processes
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
$\varepsilon$-Equilibria for Stochastic Games with Uncountable State Space and Unbounded Costs
SIAM Journal on Control and Optimization
Autonomous Bidding Agents: Strategies and Lessons from the Trading Agent Competition (Intelligent Robotics and Autonomous Agents)
Running the table: an AI for computer billiards
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Computing equilibria by incorporating qualitative models?
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Joint process games: from ratings to wikis
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Success, strategy and skill: an experimental study
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Billiards: an optimization challenge
Proceedings of The Fourth International C* Conference on Computer Science and Software Engineering
Lossy stochastic game abstraction with bounds
Proceedings of the 13th ACM Conference on Electronic Commerce
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Two-player games of billiards, of the sort seen in recent Computer Olympiads held by the International Computer Games Association, are an emerging area with unique challenges for A.I. research. Complementing the heuristic/algorithmic aspect of billiards, of the sort brought to the fore in the ICGA billiards tournaments, we investigate formal models of such games. The modeling is surprisingly subtle. While sharing features with existing models (including stochastic games, games on a square, recursive games, and extensive form games), our model is distinct, and consequently requires novel analysis. We focus on the basic question of whether the game has an equilibrium. For finite versions of the game it is not hard to show the existence of a pure strategy Markov perfect Nash equilibrium. In the infinite case, it can be shown that under certain conditions a stationary pure strategy Markov perfect Nash equilibrium is guaranteed to exist.